Optical transmission system and method for core scrambling for multicore optical fibers

ABSTRACT

The various embodiments provide an optical transmission system comprising an optical transmitter configured to transmit data over an optical fiber transmission channel made of a multi-core fiber, optical signals carrying the data propagate along the multi-core fiber according to two or more cores, each core being associated with one or more core parameters, wherein the optical transmission system comprises: a scrambling configuration device configured to determine a scrambling function depending on one or more of the core parameters associated with the two or more cores, and at least one scrambling device arranged in the optical fiber transmission channel for scrambling the two or more cores, each of the at least one scrambling device being configured to determine permuted cores by applying the scrambling function to the two or more cores and to redistribute the optical signals according to the permuted cores.

TECHNICAL FIELD

The invention generally relates to optical communications and inparticular to devices and methods for core scrambling in multi-corefibers.

BACKGROUND

The demand for more network capacity has significantly increased overthe last twenty years as a result of the development of Internet and ofthe growing traffic generated by the increasing number of internetusers. Optical fiber transmissions appear as key technologies to meetsuch continuous demand for higher transmission data rates in globaltelecommunication infrastructures.

Optical fibers represent optical waveguides that guide electromagneticwaves in the optical spectrum. The propagation of the waves along anoptical fiber depends on several parameters related to the fiber such asits geometry, its mode structure, the distribution of the refractiveindex, and the material it is made of. Optical fibers typically includea transparent core surrounded by a transparent cladding material with alower index of refraction. Light propagates in the fiber, following asuccession of internal reflections. Light carries data and allowstransmission over long distances at higher bandwidths than in wire-basedor wireless communication systems.

In the last twenty years, wavelength division multiplexing (WDM),coherent detection and polarization division multiplexing (PDM) alongwith advanced signal processing techniques marked important milestonesin the evolution of optical fiber transmission systems, enhancing boththeir capacity and their maximum reach. Nevertheless, WDM-PDM systemsusing conventional single mode fibers, with a small core radius wherewaves propagate along a single propagation mode, almost reached thenon-linear capacity limit of optical transmission systems and cannotcope with the exponential growth in the demand for higher networkbandwidth.

Promising solutions for overcoming the non-linear capacity limit ofsingle mode fibers through Space division multiplexing (SDM) exploit thespace in the fiber as the last degree of freedom available to increasethe capacity on the optical fiber transmission. Space is accordinglyused as a multiplexing dimension for the creation of a set ofindependent spatial channels over which independent data streams can bemultiplexed and carried in the same fiber. Using SDM, the capacity canbe multiplied by the number of independent spatial channels. SDMtechniques enable increasing both the reach and the transmissioncapacities of optical fiber transmission links while reducing the costof the transmission system.

Space division multiplexing can be implemented using multi-mode fibers(MMFs) or multi-core fibers (MCFs).

Multi-mode fibers allow the propagation of light according to differentspatial propagation modes. The core of a multi-mode fiber is enlarged toallow the propagation of more than one spatial mode. The number ofreflections created as the light passes through the core increases,creating the ability to propagate more data at a given time slot.

Multi-mode fibers can offer higher transmission rates than single-modefibers. However, multi-mode fibers are affected by several impairmentsmainly due to imperfections of the optical components (e.g. fibers,amplifiers, spatial mode multiplexers), the crosstalk effects betweenthe spatial modes, and non-unitary crosstalk effects known as modedependent loss (MDL).

Multi-core fibers incorporate multiple identical or different cores in asingle fiber, each core being single-mode or multi-mode. Multi-corefibers can be classified into uncoupled and coupled MCFs.

In uncoupled MCFs, each core has to be suitably arranged to keep theinter-core crosstalk sufficiently small for long distance transmissionapplications to detect signals from each core separately (i.e. nomultiple-input multiple-output equalization is required at receiver).Several types of uncoupled multi-core fibers have been designedaccording to different core arrangements. These designs comprise‘homogeneous MCFs’ and ‘homogeneous with trench-assisted MCFs’incorporating multiple identical cores, and heterogeneous MCFs'incorporating multiple cores of several types.

In coupled MCFs, several cores are placed so that they strongly and/orweakly couple with each other. Coupled MCFs supporting a single spatialmode and multiple spatial modes can be used in high-power fiber laserapplications.

Multi-core fibers are affected by several impairments due to themisalignment losses and crosstalk effects. The crosstalk andmisalignment losses induce a core dependent loss (CDL). The CDL is animpairment effect similar to the MDL affecting multi-mode fibers.

The misalignment losses rise due to the imperfections of the opticalfiber at the splices and connector part. Three types of misalignmentlosses exist comprising the longitudinal displacement losses, thetransverse displacement losses, and angular displacement losses.

The crosstalk effect is due to the existence of multiple cores in onecladding which generates a crosstalk between the neighboring cores. Thecrosstalk increases with a smaller inter-core distance and representsthe main limitation to the capacity in terms of the optical signalquality and the number of cores integrated inside a multi-core fiber.Further, low crosstalk effects enable a decoding complexity reduction atthe optical receiver since no multiple-input multiple-outputequalization is required for small crosstalk values

Optical solutions can be applied during the manufacturing of the opticalfibers in order to reduce the crosstalk effect.

A first approach consists in increasing the inter-core distance. Thisapproach enables reducing the crosstalk effect, however it limits thenumber of cores inside the fiber due to the cladding diameter andconsequently it decreases the core density and capacity.

A second approach is based on trench assistance with the use oftrench-assisted homogeneous multi-core fibers. Trench assistance reducesthe coupling coefficients by surrounding each core with a low-indextrench layer. The crosstalk in trench-assisted fiber designs isindependent of the inter-core distance.

A third solution uses heterogeneous MCFs in which an intrinsic indexdifference between neighbor cores is introduced, enabling reducing thecrosstalk effect.

Further, a random core scrambling technique, disclosed in “A. Abouseif,G. R. Ben-Othman, and Y. Jaouen, Core Mode Scramblers for ML-detectionbased Multi-Core Fibers Transmission, in Asia Communications andPhotonics Conference, OSA Technical Digest, 2017”, has been recentlyproposed to mitigate the CDL in heterogeneous trench-assisted MCFs andto enhance the system performance. It is demonstrated that random corescrambling enables achieving better performance in terms of errorprobabilities; however random scrambling requires installing a largenumber of random scramblers which induces an additional implementationcomplexity and cost on the transmission system.

Although existing solutions enable a reduction of the crosstalk inmulti-core fibers, they do not enable a complete suppression of thecrosstalk and do not provide a complete mitigation of the CDL. There isaccordingly a need for designing efficient techniques enabling acomplete mitigation of CDL effects in multi-core fibers-based SDMsystems.

SUMMARY

In order to address these and other problems, there is provided anoptical transmission system comprising an optical transmitter configuredto transmit data over an optical fiber transmission channel made of amulti-core fiber. Optical signals carrying the transmit data propagatealong the multi-core fiber according to two or more cores, each corebeing associated with one or more core parameters. The opticaltransmission system comprises:

a scrambling configuration device configured to determine a scramblingfunction depending on one or more of the core parameters associated withthe two or more cores of the multi-core fiber, and

at least one scrambling device arranged in the optical fibertransmission channel for scrambling the two or more cores, the at leastone scrambling device being configured to determine permuted cores byapplying the scrambling function to the two or more cores and toredistribute the optical signals according to the permuted cores.

In some embodiments, a core parameter associated with each core ischosen in a group comprising a core type and a core loss value.

According to some embodiments, the scrambling configuration device maybe configured to determine the core loss value associated with each coredepending on crosstalk coefficients and misalignment losses, a crosstalkcoefficient representing the crosstalk between said each core and aneighbor core to said each core, the misalignment losses representingmisalignments of the multi-core fiber.

According to some embodiments, the scrambling configuration device maybe configured to order the two or more cores according to a given orderof the core loss values associated with said two or more cores, thescrambling configuration device being configured to determine thescrambling function depending on the order of the core loss valuesassociated with said two or more cores.

According to some embodiments, the scrambling configuration device maybe configured to determine the scrambling function for permuting a coreassociated with a high core loss value with a core associated with asmall core loss value.

According to some embodiments, in which the number of the two or morecores in the multi-core fiber is an even number, the scramblingconfiguration device may be configured to determine the scramblingfunction for permuting the two or more cores two-by-two according to thepermutation of the core associated with the i^(th) highest core lossvalue with the core associated with the i^(th) lowest core loss value,with i being comprised between 1 and the half of the number of cores insaid multi-core fiber.

According to other embodiments in which the number of the two or morecores in the multi-core fiber is an odd number, the scramblingconfiguration device may be configured to determine the scramblingfunction for permuting the two or more cores two-by-two according to thepermutation of the core associated with the i^(th) highest core lossvalue with the core associated with the i^(th) lowest core loss value,with i being comprised between 1 and the floor part of half the numberof cores in the multi-core fiber.

According to some embodiments in which the multi-core fiber is anhomogeneous multi-core fiber, the two or more cores are associated withan identical core type.

According to other embodiments in which the multi-core fiber is anheterogeneous multi-core fiber, at least two of the two or more coresare associated with different core types.

According to some embodiments in which the multi-core fiber is anheterogeneous multi-core fiber, the scrambling configuration device maybe configured to determine the scrambling function depending on the coretypes associated with the two or more cores, the scrambling functioncorresponding to a two-by-two permutation of the two or more coresaccording to the permutation of at least a first core with a secondcore, the first core and the second core being associated with differentcore types.

According to some embodiments in which the multi-core fiber is anheterogeneous multi-core fiber, the scrambling configuration device maybe configured to determine the scrambling function depending on the coretypes and the core loss values associated with the two or more cores,the scrambling function corresponding to a two-by-two permutation of thetwo or more cores according to the permutation of at least a first corewith a second core, the first core and the second core being associatedwith different core types and different core loss values.

According to some embodiments, the at least one scrambling device may beconfigured to apply the scrambling function in the electrical field orin the optical field, a scrambling device configured to apply thescrambling function in the optical field being chosen in a groupcomprising optical converters, optical multiplexers, opticalmultiplexing devices, and photonic lanterns.

According to some embodiments, at least one of the two or more cores isa multi-mode core comprising two or more spatial propagation modes.

In some embodiments, the optical transmitter may comprise:

an error correcting code encoder configured to encode said data into acodeword vector by applying at least one error correcting code;

a modulator configured to determine a set of modulated symbols byapplying a modulation scheme to said codeword vectors, and

a Space-Time encoder configured to determine a codeword matrix byapplying a Space-Time code to said set of modulated symbols.

There is also provided a method for transmitting data in an opticaltransmission system over an optical fiber transmission channel made of amulti-core fiber, optical signals carrying said data propagate along themulti-core fiber according to two or more cores, each core beingassociated with one or more core parameters. The method comprisesscrambling the two or more cores, said scrambling comprises:

determining a scrambling function depending on one or more of the coreparameters associated with the two or more cores;

determining a permutation of the two or more cores by applying thescrambling function, and

redistributing the optical signals according to said permutation of thetwo or more cores.

The scrambling techniques according to the various embodiments provideefficient mitigation of crosstalk effects and misalignments losses inmulti-core fibers by averaging the losses experienced by the differentcores of the multi-core fiber.

Further advantages of the present invention will become clear to theskilled person upon examination of the drawings and the detaileddescription.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various embodiments of theinvention.

FIG. 1 illustrates a schematic diagram of an exemplary application ofthe invention in optical communication systems;

FIG. 2 illustrates a cross section of an exemplary multi-core fiber;

FIG. 3 depicts cross sections views of multi-core fibers, with a12-cores homogeneous multi-core fiber comprising twelve cores arrangedon a ring around the fiber axis and a 19-cores homogeneous fibercomprising nineteen cores arranged in a two-dimensional grid comprisinga central core, according to some embodiments;

FIG. 4 depicts a cross section view of a multi-core fiber, according tosome embodiments in which the multi-core fiber is a 12-cores homogeneoustrench-assisted multi-core fiber;

FIG. 5 illustrates a cross section view of a multi-core fiber, accordingto some embodiments in which the multi-core fiber is a 12-coresheterogeneous multi-core fiber comprising twelve cores arranged on aring around the fiber axis;

FIG. 6 illustrates cross sections views of multi-core fibers, with a7-cores heterogeneous fiber comprising seven cores and a 19-coresheterogeneous fiber comprising three groups of cores, the cores of eachthe different groups having different types, according to an embodiment;

FIG. 7 illustrates cross sections view of multi-core fibers, with a12-cores heterogeneous trench-assisted multi-core fiber comprisingtwelve cores arranged on a ring around the fiber axis and a 7-coresheterogeneous trench-assisted, according to some embodiments;

FIG. 8 is a block diagram illustrating the structure of an opticaltransmitter according to some embodiments of the invention;

FIG. 9 is a block diagram illustrating the structure of an opticalreceiver according to some embodiments of the invention;

FIG. 10 is a flowchart illustrating a method for transmitting data overan optical transmission channel, according to some embodiments in whichcore scrambling is performed;

FIG. 11 illustrates a cross section view of a multi-core fiber,according to some embodiments in which a snail scrambling technique isconsidered;

FIG. 12 illustrates a cross section view of a multi-core fiber,according to some embodiments in which a rotation scrambling techniqueis considered;

FIG. 13 illustrates a cross section view of a multi-core fiber,according to some embodiments in which a snake scrambling technique isconsidered;

FIG. 14 shows two diagrams representing the core dependent loss as afunction of the number of scramblers in some embodiments in which asnail scrambling technique is considered;

FIG. 15 shows two diagrams representing the core dependent loss as afunction of the number of scramblers in some embodiments in which arotation scrambling technique is considered;

FIG. 16 shows two diagrams representing the core dependent loss as afunction of the number of scramblers in some embodiments in which asnake scrambling technique is considered;

FIG. 17 shows diagrams representing the bit error rate (BER) performanceobtained for a multi-core fiber implementing a snail scramblingtechnique;

FIG. 18 shows diagrams representing the bit error rate (BER) performanceobtained for a multi-core fiber implementing a rotation scramblingtechnique, and

FIG. 19 represents the bit error rate (BER) performance obtained for amulti-core fiber implementing a snake scrambling technique.

DETAILED DESCRIPTION

Embodiments of the present invention provide a multi-core optical fibertransmission system implementing efficient deterministic scramblingdevices and methods enabling a reduction of the crosstalk andmisalignment losses impacting the multi-core fiber.

Devices and methods according to the various embodiments of theinvention may be implemented in optical fiber transmission systemsapplied to a wide variety of applications. Exemplary applicationscomprise, without limitation, optical fiber communications, aerospaceand avionics, data storage, automotive industry, imaging,transportation, sensing, and photonics.

Exemplary communication applications comprise desktop computers,terminals, and nationwide networks. Optical fibers may be used totransmit light and thus information/data over short distances (less thanone meter) or long distances (up to hundreds or thousands of kilometersfor example in communications over metropolitan networks, wide areanetworks, transoceanic links). Such applications may involve transfer ofvoice (e.g. in telephony), data (e.g. data supply to homes and officesknown as fiber to the home), images or video (e.g. transfer of internettraffic), or connection of networks (e.g. connection of switches orrouters and data center connectivity in high-speed local area networks).

In an exemplary implementation of the invention in the field ofaerospace and avionics industries, optical fiber-based products may beused in military and/or commercial applications. Optical fibertechnologies and products are designed in such applications to meetrigorous testing and certifications requirements in harsh environmentsand conditions.

In an exemplary implementation of the invention in data storageapplications, optical fibers may be used in data storage equipments as alink between multiple devices in a network and/or as part of a storagesystem. Optical fiber connectivity offers very high bandwidth even overextended distances.

In another exemplary application of the invention to automotiveindustry, optical fiber technologies may be used for example inlighting/illumination, communications, and sensing for safety andcontrol devices and systems.

In still another exemplary application of the invention to imagingapplications (e.g. telemedicine), the optical transmission properties ofthe optical fibers may be used to transmit an image of a target or asubject area to the image view end for analysis and/or interpretation.

The invention may be used also in transportation systems, in which smarthighways with intelligent traffic lights, automated tollbooths andchangeable message signs may use telemetry systems based on opticalfibers.

The invention may further be used in sensing applications, where opticalfiber sensors are used for sensing some quantities such as temperatures,displacements, vibrations, pressure, acceleration, rotations, andconcentration of chemical species. Exemplary applications of opticalfiber sensors comprise sensing in high voltage and high-power machineryor in microwaves, distributed temperature and strain measurements inbuildings for remote monitoring (e.g. monitoring of the wings ofairplanes, wind turbines, bridges, pipelines), downhole sensing in oilexploration applications, etc.

In another application of the invention to photonics, optical fibers maybe used for connecting components in optical fiber devices, such asinterferometers and fiber lasers. In such application, optical fibersplay a similar role as electrical wires do in electronic devices.

The following description of certain embodiments will be made withreference to communication applications, for illustration purposes only.However, the skilled person will readily understand that the variousembodiments of the invention may be applied to other types of systemsfor different applications.

FIG. 1 illustrates an exemplary implementation of the invention in anoptical transmission system 100 (also referred to as ‘opticalcommunication system’) based on optical fiber transmissions. The opticaltransmission system 100 comprises at least one optical transmitterdevice 11 (hereinafter referred to as an “optical transmitter”)configured to encode an input data sequence into an optical signal andtransmit the optical signal optically to at least one optical receiverdevice 15 (hereinafter referred to as an “optical receiver”) through anoptical fiber transmission channel 13 (hereinafter referred to as an‘optical fiber link’) configured to transmit the light over somedistance.

The optical communication system 100 may comprise computers and/orsoftwares to control the system operability.

The optical fiber transmission channel 13 comprises a multi-core fibercomprising a concatenation of a plurality of fiber sections 131 (alsoreferred to as ‘fiber span’ or ‘fiber slice’). The fiber sections 131may be aligned or misaligned.

The multi-core fiber is a cylindrical non-linear waveguide consisting oftwo or more cores, a cladding surrounding the two or more cores, and acoating. Each core has a refractive index. The optical signal sent bythe optical transmitter 11 is multiplexed and is guided in each core ofthe multi-core fiber through total internal reflections due to thedifference between the refractive indices of the cores and therefractive index of the cladding.

In some embodiments in which the multi-core fiber is an uncoupled fiber,each core of the multi-core fiber may act as a separate waveguide suchthat the optical signal can be considered as propagating independentlytrough the cores.

In some embodiments in which the multi-core fiber is a coupled fiber,some coupling may exist between the cores if the distance between twocores is so small that the optical signals propagating along thedifferent cores overlap.

The optical fiber may be made of glass (e.g. silica, quartz glass,fluoride glass), typically for long-distance transmissions. For shortdistance transmissions, the optical fiber may be a plastic opticalfiber.

The multi-core fiber may be characterized by geometrical parameters andoptical parameters. Geometrical parameters may comprise the claddingdiameter, the core-to-core distance, and the core-outer claddingdistance. Optical parameters may comprise the wavelength, the crosstalkcoefficients representing the crosstalk between the different cores ofthe multi-core fiber, and the refractive index difference between eachcore and the cladding.

In some embodiments, the optical fiber communication system 100 mayoperate in a wavelength region corresponding to a region chosen in agroup comprising:

-   -   the window of wavelengths ranging in 800-900 nm, suitable for        short-distance transmissions;    -   the window of wavelengths around 1.3 μm, used for example for        long-haul transmissions;    -   the window of wavelengths around 1.5 μm, more used since the        losses of silica fibers are lowest in this wavelength region.

FIG. 2 depicts a cross section of a six-cores fiber, D_(clad)representing the cladding diameter, d_(c-c) designating the inter-coredistance, and d_(c-Clad) representing the core-outer cladding distance.

In some embodiments, the cores in the multi-core fiber may be arrangedon a ring around the fiber axis for example on the edges of a hexagon.In other embodiments, the cores may be arranged on some 2-dimensionalgrid.

In an embodiment, the multi-core fiber may be a homogeneous multi-corefiber comprising two or more cores of identical types.

FIG. 3 depicts two cross sections of two exemplary homogeneousmulti-core fibers, a first 12-cores fiber comprising 12 cores ofidentical types arranged on a ring around the fiber axis, and a second19-cores fiber comprising 18 cores arranged on the edges of the hexagonand a central core.

In an embodiment, the multi-core fiber may be a homogeneoustrench-assisted multi-core fiber, each core being surrounded by alow-index trench layer.

FIG. 4 illustrates a cross section of an exemplary trench-assistedhomogeneous multi-core fiber comprising 12 cores of identical types.

In another embodiment, the multi-core fiber may be a heterogeneousmulti-core fiber comprising a plurality of cores among which at leasttwo cores are of different types.

FIG. 5 illustrates a cross section of an exemplary heterogeneousmulti-core fiber comprising 12 cores among which cores numbered 2i+1with i=0, . . . ,5 are identical, the cores numbered 2i+2 with i=0, . .. ,5 are identical, and the cores numbered 2i+1 are of a core typedifferent from the core type of the cores numbered 2i+2 for i=0, . . .,5. Each core in such heterogeneous multi-core fiber has two neighbors,each core having a core type different from the core type of itsneighbor cores.

FIG. 6 illustrates two cross sections of two exemplary 7-cores fiber and19-cores heterogeneous fibers. The 7-cores fiber comprises six cores onthe edges of the hexagon numbered 1-6 and a central core numbered 7.This 7-cores fiber involves three different core types, the central corehaving a core type different from the types of the cores on the edges ofthe hexagon, and each core arranged on the edges of the hexagon having acore type different from the core type of its neighbor cores. The19-cores fiber comprises three different core types, the central corehaving a core type different from the types of the cores on the edges ofthe hexagon.

In an embodiment, the multi-core fiber may be a trench-assistedheterogeneous multi-core fiber.

FIG. 7 depicts cross sections of two exemplary 12-cores and 7-corestrench-assisted heterogeneous multi-core fibers.

In some embodiments, each core of the multi-core fiber may be singlemode comprising one spatial propagation mode.

In some embodiments, the multi-core fiber may comprise at least onemulti-mode core comprising two or more spatial propagation modes.

In some embodiments, each core in the fiber may be associated with oneor more core parameters, a core parameter being chosen in a groupcomprising a core type and a core loss value, the core value quantifyingthe loss experienced by the core in terms of the inter-core crosstalk(e.g. the crosstalk between the core and its neighbor cores) and themisalignment losses.

The optical fiber transmission channel 13 may further comprise one ormore amplifiers 132 inserted in the fiber for re-amplifying the opticalpower and compensating for the fiber attenuation without the need toregenerate the optical signals such that a sufficient signal power canbe maintained over large distance where optical signals need to beperiodically amplified.

The amplifiers 132 may be inserted between each pair of fiber slices131. In particular, an amplifier 132 inserted at the end of the opticalfiber transmission channel performs signal amplification before signaldetection at the receiver 15.

Each amplifier 132 may be configured to simultaneously amplify theoptical signal corresponding to the plurality of cores in the multi-corefiber.

In some embodiments, the amplifiers 132 may consist of a duplication ofa single core fiber amplifier.

In other embodiments, an amplifier 132 may be an optical multi-coreamplifier. Exemplary optical amplifiers comprise multi-core Erbium dopedfiber amplifiers (EDFAs) such as core-pumped multi-core EDFAs andcladding-pumped EDFA amplifiers. Core-pumped and cladding pumpedamplifiers may use a single or a plurality of pump diodes. Inparticular, a pump diode per core may be used in EDFA amplifiers.

In some embodiments, the optical signal amplification may be performedin a distributed manner using the non-linear simulated Raman scatteringeffect. In such embodiments, the fiber is used as both a transmissionlink and an amplification medium.

In other embodiments, signal amplification may be achieved by a jointuse of regularly arranged optical amplifiers and of simulated RamanScattering effects.

In still other embodiments, the signal amplification may be performed inthe electrical domain through an optical/electrical conversion (notillustrated in FIG. 1). In such embodiments, the optical fibertransmission channel 13 may comprise, at each amplification stage:

-   -   a photodiode for converting the optical signal back to the        electrical domain;    -   an electrical amplifier for amplifying the converted electrical        signal; and    -   a laser diode for generating an optical signal corresponding to        the amplified electrical signal.

According to some embodiments (not illustrated in FIG. 1), the opticaltransmission channel 13 may further comprise one or more of:

-   -   dispersion compensators for counteracting the effects of        chromatic dispersion, a dispersion compensator being configured        to cancel the chromatic dispersion or compensate the dispersion        for example before the detection of the optical signal at the        receiver 15;    -   optical switches and multiplexers such as optical add/drop        multiplexers implemented in wavelength division multiplexing        systems;    -   one or more devices for regenerating the optical signal such as        electronic and optical regenerators.

In some embodiments in which core scrambling is performed in the opticaldomain using optical devices, optical multiplexers may be used as corescramblers.

FIG. 8 shows the components of an optical transmitter 11 according tosome embodiments. The optical transmitter 11 may be configured totransform an input data sequence into an optical signal to betransmitted through the optical transmission channel 13. Accordingly,the optical transmitter 11 may comprise:

-   -   a Forward Error Correcting code (FEC) encoder 81 (also referred        to as ‘an error correcting code encoder 81’) configured to        encode an input data sequence of length k (i.e. comprising k        symbols) into an encoded sequence in the form of a codeword        vector of length n>k by applying at least one Forward Error        Correcting code (FEC) (also referred to as ‘an error correcting        code’);    -   an interleaver 83 configured to mix the encoded sequence to add        a protection layer to the encoded symbols against burst errors        before being modulated;    -   a modulator 85 configured to determine a set of modulated        symbols in a form of a modulated symbol vector s_(c) by applying        a modulation scheme. to the interleaved encoded sequence (or to        the codeword vectors in embodiments where the transmitter 11        does not comprise an interleaver). Different modulation schemes        may be implemented such as 2^(q)-QAM or 2^(q)-PSK with 2^(q)        symbols or states. The modulated vector 5, may be a        complex-value vector comprising κ complex-value symbols s₁,s₂, .        . . ,s_(κ) with q bits per symbol. When Modulation formats such        as 2^(q)-QAM are used, the 2^(q) symbols or states represent a        sub-set of the integer field        [i]. The corresponding constellation is composed of 2^(q) points        representing the different states or symbols. In addition, in        the case of squared modulations, the real and imaginary parts of        the information symbols belong to the same finite alphabet        A=[−(q−1), (q−1)];    -   a Space-Time Encoder 87 configured to determine a codeword        matrix carrying the data symbols to be sent through the optical        transmission channel 13 during a Time Transmission Interval        (TTI) by applying a Space-Time code. The Space-Time encoder 25        may be configured to transform each received sequence (or block)        of Q modulated symbols s₁, s₂, . . . ,s_(Q) into a codeword        matrix X of dimensions N_(t)×T. A codeword matrix comprises        complex values arranged in N_(t) rows and T columns where N_(t)        designates the number of propagation cores used for propagating        optical signals and T designates the temporal length of the        Space-Time code and corresponds to the number of temporal        channel uses. Each value of a codeword matrix accordingly        corresponds to a time of use and to a propagation core used for        the signal propagation. The Space-Time Encoder 87 may use a        linear Space-Time Block Code (STBC) to generate the codeword        matrix. The coding rate of such codes is equal to

$\frac{\kappa}{T}$

complex symbols per channel use, where κ is the number of encodedcomplex-value symbols composing the vector s_(c)=[s₁, s₂, . . .,s_(κ)]^(t) of dimension κ in this case. When full-rate codes are used,the Space-Time Encoder 87 encodes κ=N_(t)T complex-value symbols.Examples of STBCs are the Perfect Codes. The Perfect Codes provide fullcoding rates by encoding a number κ=N_(t) ² (T=N_(t)) of complexinformation symbols and satisfy a non-vanishing determinant property.

In some embodiments, the Space-Time Encoder 87 may use a spatialmultiplexing scheme known as V-BLAST scheme by multiplexing the receivedcomplex-value information symbols over the different propagation cores,without performing a coding in the time dimension.

According to some embodiments, the input data sequence may be a binarysequence comprising k bits. The FEC encoder 81 may be configured, insuch embodiments, to encode the input binary sequence into a binarycodeword vector comprising n bits by applying at least one binary FECcode.

In other embodiments, the input data sequence may comprise symbols thattake values in a Galois Field GF(q) with q>2 representing the order ofthe Galois Field. In such embodiments, the FEC encoder 22 may beconfigured to encode the input data sequence into a codeword vectorcomprising n symbols, each symbol comprised in the codeword vector takesvalue in the Galois Field GF(q). The encoding process in this case maybe performed using a non-binary FEC code constructed over GF(q) withq>2.

By performing the coding operation, the FEC encoder 81 adds redundantbits (in general redundant symbols) to the input binary sequence so thatthe receiver can detect and/or correct common transmission errors. Theuse of a FEC code provides an additional protection and immunity againsttransmission errors and allows significant improvement in performancewith respect to uncoded transmission (i.e. transmission of modulateddata without FEC encoding).

Additional improvements and reduction on the probability of error may beachieved through the concatenation of two or more FEC codes.Concatenation of codes may follow a serial, a parallel, or a multi-levelarchitecture. The FEC encoder 81 may be accordingly configured toimplement two or more FEC codes.

The optical transmitter 11 may further comprise a plurality ofmulti-carrier modulators 88 configured to generate multi-carrier symbolsby implementing a multi-carrier modulation technique within each opticalcarrier involving a large number of orthogonal sub-carriers. Moreover,multi-carrier modulations may be implemented for providing a betterresistance to the inter-symbol interference resulting from the fiberdispersion and crosstalk between the various cores in the multi-corefiber. Exemplary multi-carrier modulation formats comprise OrthogonalFrequency Division Multiplexing (OFDM) and Filter Bank Multi-Carrier(FBMC).

The frequency-domain signal delivered by the multicarrier modulators 88may be then processed by a digital-optical Front-End 89 configured toconvert the received frequency-domain signal to the optical domain. Thedigital-optical Front-End 88 may perform the conversion using a numberof lasers of given wavelengths and a plurality of optical modulators(not shown in FIG. 8) associated with the used polarization states andthe spatial propagation modes in the cores of the multi-core fiber. Alaser may be configured to generate a laser beam of a same or differentwavelength using Wavelength Division Multiplexing (WDM) techniques. Thedifferent laser beams may be then modulated using the different outputsof the OFDM symbols (or the different values of the codeword matrix inembodiments using single-carrier modulations) by means of the opticalmodulators and polarized according to the different polarization statesof the fiber. Exemplary modulators comprise Mach-Zehnder modulators. Aphase and/or amplitude modulation may be used. In addition, themodulation scheme used by the various optical modulators for modulatingthe different optical signals may be similar or different.

The number of the optical modulators and lasers depends on the number ofused polarization states, the number of used propagation modes in eachcore of the multi-core fiber, and on the number of cores in the fiber.

The digital-optical front-end 88 may further comprise a FAN-IN device(not illustrated in FIG. 8) configured to inject the generated opticalsignals into each core of the multi-core fiber to propagate according tothe available propagation modes in each core. Optical connectors may beused to connect the output end of the FAN-IN device and the input end ofthe multi-core optical transmission channel 13.

The optical signals generated according to any of the precedingembodiments may propagate along the fiber until reaching the other endof the optical transmission channel 13 where it is processed by anoptical receiver 15.

FIG. 9 is a block diagram of an optical receiver 15 according to someembodiments. The optical receiver 15 is configured to receive theoptical signal transmitted by the optical transmitter 11 through thetransmission channel 13 and to generate an estimate of the originalinput data sequence. Accordingly, the optical receiver 15 may comprise:

-   -   an optical-digital front-end 91 configured to detect the optical        signals, using for example one or more photodiodes, and to        convert them into a digital signal. The optical-digital        front-end 91 may comprise a FAN-OUT device (not illustrated in        FIG. 9);    -   a plurality of multi-carrier demodulators 92 configured to        remove the cyclic prefix and generate a set of decision        variables to be delivered to the Space-Time decoder 93;    -   a Space-Time decoder 93 configured to generate an estimate of        the modulated data sequence from the set of decision variables        by applying a Space-Time decoding algorithm;    -   a demodulator 94 configured to generate a binary sequence by        performing a demodulation of the modulated data sequence        estimated by the Space-Time decoder 93;    -   a de-interleaver 95 configured to rearrange the order of the        bits (in general the symbols) in the binary sequence delivered        by the demodulator 94 to restore the original order of the bits;        and    -   a FEC decoder 96 (also referred to as ‘an error correcting code        decoder 96’) configured to deliver an estimate of the input data        sequence processed by the optical transmitter device 11 by        applying a soft or hard-decision FEC decoder to the reordered        binary sequence delivered by the de-interleaver 95. Exemplary        soft-decision FEC decoders comprise the Viterbi algorithm.

The Space-Time decoder 93 may implement a Space-Time decoding algorithmchosen in a group consisting of a maximum likelihood decoder, aZero-Forcing decoder, a Zero-Forcing Decision Feedback Equalizer, and aMinimum Mean Square Error decoder.

Exemplary maximum likelihood decoders comprise the sphere decoder, theSchnorr-Euchner decoder, the stack decoder, the spherical-bound-stackdecoder.

In embodiments using single-carrier modulations, the plurality ofmulti-carrier modulators 92 may be replaced by a single modulator.Similarly, the multi-carrier demodulators 92 may be replaced by a singledemodulator.

In some embodiments in which the FEC encoder 81 implements aconcatenation of two or more forward error correcting codes, acorresponding structure may be implemented by the FEC decoder 96. Forexample, in embodiments based on a serial concatenation of an inner codeand an outer code, the FEC decoder 96 may comprise an inner codedecoder, a de-interleaver, and an outer code decoder (not shown in FIG.9). In embodiments involving two codes in a parallel architecture, theFEC decoder 96 may comprise a de-multiplexer, a de-interleaver, and ajoint decoder (not shown in FIG. 9).

The following description of certain embodiments of the invention willbe made with reference to an optical communication system 100 using asingle polarization, a single wavelength, a single carrier-modulation, asingle error correcting code without Space-Time Coding, and asingle-mode multi-core fiber, for illustration purposes only. However,the skilled person will readily understand that the various embodimentsof the invention can also be applied in multi-core fibers in combinationwith polarization multiplexing using two polarizations and/or incombination with wavelength multiplexing using a plurality ofwavelengths, and/or in combination with mode multiplexing usingmulti-mode fiber cores, and/or in combination with multi-carriermodulation formats, and/or in combination with Space-Time coding.

To facilitate the understanding of some embodiments of the invention,there follows some notations and/or definitions used hereinafter:

-   -   L designates the total length of the multi-core fiber in the        optical fiber transmission channel 13;    -   K designate the number of fiber sections composing the        multi-core fiber;    -   d designates a correlation length;    -   R_(b) designates a bending radius;    -   N_(c)≥2 designates the total number of cores in the multi-core        fiber, the cores being numbered (i.e. each core being associated        with a core number varying between 1 and N_(c)) such that the a        core is designated as core-n with n taking value between 1 and        N_(c);    -   R_(n), designates the radius of core-n;    -   the core parameters associated with the core-n with n=1, . . .        ,N_(c) are denoted by {T_(n);λ_(n)} with T_(n) designating the        core type of core-n and λ_(n) designating a core loss value        associated with the core-n;    -   XT_(n,m) refers to a crosstalk coefficient quantifying the        crosstalk between the core-n and the core-m with n≠m;    -   k_(n,m) refers to a coupling coefficient quantifying the        coupling between the core-n and the core-m with n≠m;    -   Δβ_(nm) stands for the propagation constant difference between        the core-n and the core-m with n≠m;

The various embodiments of the invention provide efficient scramblingtechniques to reduce the core-related impairments and mitigate of thecore dependent loss affecting the multi-core fiber by performing adeterministic scrambling of the cores in the multi-core fiber enablingto average the core dependent loss experienced by the cores.

In some embodiments, the optical transmission system 100 may comprise:

-   -   a scrambling configuration device 17 configured to determine a        scrambling function depending on one or more of the core        parameters associated with the N_(c)≥2 cores comprised in the        multi-core fiber, and    -   at least one scrambling device 133 arranged in the optical fiber        transmission channel 13 for scrambling the N_(c)≥2 cores        comprised in the multi-core fiber, each of the at least one        scrambling device 133 being configured to determine permuted        cores by applying the scrambling function determined by the        scrambling configuration device 17 to the N_(c)≥2 cores and to        redistribute the optical signals propagating along the        multi-core fiber according to the permuted cores.

According to some embodiments, a core parameter associated with eachcore core-n may be chosen in a group comprising a core type T_(n) and acore loss value λ_(n).

The following description will be made with reference to a multi-corefiber in which each core core-n is associated with the set of coreparameters {T_(n);λ_(n)} comprising the core type T_(n) and a core lossvalue λ_(n), for illustration purposes.

The optical transmission channel 13 may be represented by an opticalmultiple-input multiple-output (MIMO) system described by the relation:

Y=H·X+N  (1)

In equation (1):

-   -   X designates a complex-value vector of length N_(c) comprising        N_(c) symbols transmitted over the optical transmission channel        13 such that the n^(th) symbol is transmitted over the core-n        with n=1, . . . ,N_(c);    -   Y is a complex-value vector of length N_(c) designating the        received signal at the optical receiver 15,    -   H is a complex-value matrix of dimensions N_(c)×N_(c)        designating the optical channel matrix and representing the        undergone attenuations and the losses experienced by the cores        during the optical signal propagation over the different cores        in the multi-core fiber in addition to the misalignment losses,        and    -   N is a real-value vector of length N_(c) designating the optical        channel noise.

According to some embodiments, the optical channel noise may be a WhiteGaussian Noise of zero-mean and variance N₀.

According to some embodiments, the optical fiber transmission channel 13experiences inter-core crosstalk effects and misalignment effects.

The inter-core crosstalk effects may be represented by a cross-talkchannel matrix denoted by H_(XT) expressed according to:

$\begin{matrix}{H_{XT} = \begin{bmatrix}{XT}_{1} & {XT}_{1,2} & \ldots & {XT}_{1,N_{c}} \\{XT}_{2,1} & \ddots & \ldots & {XT}_{2,N_{c}} \\\vdots & \vdots & \ddots & \vdots \\{XT}_{N_{c},1} & {XT}_{N_{c},2} & \ldots & {XT}_{N_{c},N_{c}}\end{bmatrix}} & (2)\end{matrix}$

In equation (2), the diagonal entries of the crosstalk channel matrixare given by XT_(n)=1 Σ_(n≠m)XT_(n,m). The crosstalk represents theexchanging energy between the cores and can be estimated based on thecoupled-power theory, known to the person skilled in the art.

According to some embodiments in which the multi-core fiber ishomogeneous, the crosstalk coefficients XT_(n,m) quantifying thecrosstalk between each core-n and core-m with n≠m are expressedaccording to:

$\begin{matrix}{{XT}_{n,m} = {\frac{2k_{n,m}^{2}R_{b}}{\Lambda\beta^{2}}L}} & (3)\end{matrix}$

In equation (3), Λ designates the core-to-core distance and β² refers tothe propagation constant.

According to some embodiments in which the multi-core fiber isheterogeneous, the crosstalk coefficients XT_(n,m) quantifying thecrosstalk between each core-n and core-m with n≠m according to:

$\begin{matrix}{{XT_{n,m}} = {\frac{2k_{n,m}^{2}}{{\Delta\beta}_{n,m}^{2}d}L}} & (4)\end{matrix}$

In some embodiments, the misalignment losses may rise due to theimperfections of the optical fiber at the fiber spans and of theconnectors (e.g. the connectors between the FAN-IN/FAN-OUT devices andthe input/output ends of the optical fiber transmission channel).Misalignment losses may comprise longitudinal misalignments, transversemisalignments, and angular misalignments.

According to some embodiments, the misalignment losses may be modeled asrandom Gaussian variables. More specifically, the misalignment lossassociated with core-n may be modeled as a random Gaussian variable ofzero-mean and a standard deviation denoted by σ_((x,y),n) expressedaccording to:

$\begin{matrix}{\sigma_{{({x,y})},n} = \frac{r_{d}}{R_{n}}} & (5)\end{matrix}$

In equation (5), r_(d) designates the transverse displacement of themulti-core fiber in the ‘x’ and ‘y’ directions.

According to some embodiments, the scrambling configuration device 17may be configured to determine the core loss value λ_(n) associated witheach core core-n for n=1, . . . ,N_(c) depending on at least onecrosstalk coefficients XT_(n,m) for m≠n and at least one misalignmentloss value (also referred to ‘misalignment loss coefficient’), thecrosstalk coefficient XT_(n,m) representing the crosstalk between thecore-n and a neighbor core core-m to the core core-n and themisalignment losses coefficients representing the misalignments of themulti-core fiber.

According to some embodiments, the scrambling configuration device 17may be configured to determine the core loss value λ_(n) associated witheach core core-n for n=1, . . . ,N_(c) by applying a singular valuedecomposition to the optical channel matrix H. In particular, thescrambling configuration device 17 may be configured first to perform aQR decomposition of the optical channel matrix according to:

H=QR  (6)

In equation (6), Q is a N_(c)×N_(c) orthogonal matrix and R is aN_(c)×N_(c) upper triangular matrix. The values of the diagonal entriesof the upper triangular matrix R are given by:

R _(ii)=α_(i)√{square root over ((XT _(i))²+Σ_(j=1) ^(N) ^(c) (XT_(i,j))²)}  (7)

In equation (7), α_(i) designates the total misalignment loss associatedwith the core core-i and XT_(i)=1−Σ_(i≠m) XT_(i,m) designates a totalcrosstalk coefficient quantifying the total crosstalk associated withthe core core-i at the end of the optical transmission channel 13, thetotal crosstalk coefficient associated with the core core-i beingdependent on the crosstalk coefficients quantifying the crosstalkbetween said core core-i and the remaining cores in the multi-corefiber.

Using the QR decomposition of the optical channel matrix, the singularvalue decomposition of the optical channel matrix can be expressedaccording to:

H=U·Σ·V  (8)

In equation (8), the matrix Σ is a N_(c)×N_(c) diagonal matrix given by:

$\begin{matrix}{\sum{= \begin{bmatrix}{\alpha_{1}{XT}_{1}} & \; & \ldots & 0 \\\vdots & \; & \ddots & \vdots \\0 & \ldots & \alpha_{N_{c}} & {XT}_{N_{c}}\end{bmatrix}}} & (9)\end{matrix}$

The multi-core fiber is made of a concatenation of K fiber spans, eachspan is equivalent to a multiplication of a crosstalk channel matrix anda misalignment channel matrix. Accordingly, the optical MIMO system ofequation (1) can be equivalently expressed according to:

Y=√{square root over (L)}Π_(k=1) ^(K)((H _(XT,k))M _(k))X+N  (10)

In equation (10):

-   -   L designates a normalization factor used to compensate the        optical fiber link loss;    -   H_(XT,k) designates the crosstalk channel matrix associated with        the k^(th) fiber span, and    -   M_(k) designates the misalignment channel matrix associated with        the k^(th) fiber span.

Using the fiber decomposition into fiber spans, the misalignment lossescoefficients α_(i) may be given by:

α_(i)=Π_(k=1) ^(K)α_(i) ^(k) =c·exp(Z _(i)); Z _(i)=Σ_(k=1) ^(K) −b(dx_(k,i) ² +dy _(k,i) ²)  (11)

In equation (11), c designates a constant multiplication factor,dx_(k,i) ² and dy_(k,i) ² for i=1, . . . ,N_(c) designate Chi-squareddistributed random variables with one degree of freedom, a mean valueequal to (σ_((x,y),i))², and a variance equal to 2(σ_((x,y),i))⁴.

Considering embodiments in which the number of fiber spans K is high,the inventors showed that the variable Z can be modeled as a normallydistributed variable with mean μ_(Z) _(i) =−2Kb(σ_((x,y),i))² andvariance σ_(Z) _(i) ²=4Kb²σ_((x,y),i) ⁴. Accordingly, the total lossescoefficients α_(i) can be modeled by a lognormal random variable with amean value μ_(α) _(i) and a variance value σ_(α) _(i) ² givenrespectively by:

μ_(α) _(i) =exp(μZ _(i)+σ_(Z) _(i) ²/2)  (12)

σ_(α) _(i) ²=(exp(σ_(Z) _(i) ²)−1)·μ_(α) _(i) ²  (13)

According to the derivation of the singular value decomposition of theoptical channel matrix, the optical MIMO system of equation (1) can beexpressed according to:

$\begin{matrix}{Y = {{{{\sqrt{L} \cdot U \cdot \begin{bmatrix}{\alpha_{1}{XT}_{1}} & \; & \ldots & 0 \\\vdots & \; & \ddots & \vdots \\0 & \ldots & \alpha_{N_{c}} & {XT}_{N_{c}}\end{bmatrix}}{V \cdot X}} + N} = {{{\sqrt{L} \cdot U \cdot \begin{bmatrix}\lambda_{1} & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \ldots & \lambda_{N_{c}}\end{bmatrix}}{V \cdot X}} + N}}} & (14)\end{matrix}$

According to equation (14), the scrambling configuration device 17 maybe configured to determine the core loss value λ_(n) associated witheach core core-n, for n=1, . . . ,N_(c), such that the core loss valueλ_(n) is a lognormally distributed variable with mean μ_(λ) _(n) =μ_(α)_(n) XT_(n) and variance σ_(λ) _(n) ²=σ_(α) _(n) ²XT_(n), the mean andthe variance of each core loss value being dependent on the totalcrosstalk coefficient XT_(n) associated with said each core and on themisalignment losses rising in the mean and the variance of the lognormaldistribution of the misalignment losses coefficients α_(i).

According to some embodiments, the core scrambling may be performeddepending on the core loss values for averaging the losses experiencedby the different cores, the scrambling function being accordingly to ascrambling criterion that depends on the core loss values.

In such embodiments, the scrambling configuration device 17 may beconfigured to order the N_(c)≥2 cores comprised in the multi-core fiberaccording to a given order (increasing or decreasing) of the core lossvalues associated with said cores. The cores core-i for i taking valuebetween 1 and N_(c) may be accordingly ordered in a numbered listdenoted by

=({core₁,{T₁,λ₁}},{core₃,{T₂,λ₂}},{core₃,{T₃,λ₃}}, . . . ,{core_(N) _(c),{T_(N) _(c) ,λ_(N) _(c) }}) such that each core core_(i) in thenumbered list

is associated with a core loss value λ_(i) higher than or smaller thanthe core loss value λ_(i+1) associated with the core core_(i+1)depending on the given order considered to order the cores.

For example, for an increasing order of the core loss values, the corescore_(i) are ordered in the list such that the core loss value λ_(i)associated with the core core_(i) is smaller than or equal to the coreloss value λ_(i+1) associated with the core core_(i+1), that isλ_(i)≤λ_(i+1) for i=1, . . . ,N_(c)−1.

In embodiments using a decreasing order of the core loss values, thecores core_(i) may be ordered in the list such that the core loss valueλ_(i) associated with the core core_(i) is higher than or equal to thecore loss value λ_(i+1) associated with the core core_(i+1), that isλ_(i)>λ_(i+1) for i=1, . . . ,N_(c)−1.

Given the order of the core loss values, the scrambling configurationdevice 17 may be configured to determine a scrambling function denotedby it depending on the order of the core loss values associated with thetwo or more cores.

Using the notation of the numbered list, the scrambling configurationdevice 17 may be configured to determine the scrambling function π forpermuting a core core_(i) with a core core_(j) in the numbered list withi taking value between 1 and N_(c) and j=N_(c)−i+1. Accordingly, thescrambling function π may enable permuting the core core₁ with the corecore_(N) _(c) , permuting the core core₂ with the core core_(N) _(c)_(−i), etc such that the core associated with the first highest coreloss value is permuted with the core associated with the first lowestcore loss value, the core associated with the second highest core lossvalue is permuted with the core associated with the second lowest coreloss value, so on.

In some embodiments in which the number N_(c)≥2 of cores in themulti-core fiber is an even number, the scrambling configuration device17 may be configured to determine the scrambling function for permutingthe two or more cores two-by-two according to the permutation of thecore core_(i) associated with the i^(th) highest core loss value withthe core core_(N) _(c) _(−i+1) associated with the i^(th) lowest coreloss value, with i being comprised between 1 and the half of the numberof cores in the multi-core fiber, that is

${i = 1},\ldots\mspace{14mu},{\frac{N_{c}}{2}.}$

In other embodiments in which the number N_(c)≥2 of cores in themulti-core fiber is an odd number, the scrambling configuration device17 may be configured to determine the scrambling function for permutingthe two or more cores two-by-two according to the permutation of thecore core_(i) associated with the i^(th) highest core loss value withthe core core_(N) _(c) _(−i+1) associated with the i^(th) lowest coreloss value, with i being comprised between 1 and the floor part of halfthe number of cores in said multi-core fiber, that is

${i = 1},\ldots\mspace{14mu},\left\lfloor \frac{N_{c}}{2} \right\rfloor,$

the operator └.┘ designating the floor operation. Accordingly, the core

${core}_{{\lfloor\frac{N_{c}}{2}\rfloor} + 1}$

may not be permuted.

In particular, in some embodiments in which the cores are arranged inthe fiber according to a 2D grid, the core

${core}_{{\lfloor\frac{N_{c}}{2}\rfloor} + 1}$

may correspond to the central core.

The determination of the scrambling function depending on the core lossvalues may be performed for optical transmission systems using ahomogeneous or a heterogeneous multi-core fiber.

According to some embodiments in which the multi-core fiber is aheterogeneous multi-core fiber, the scrambling configuration device 17may be configured to determine the scrambling function π depending onthe core types T_(n) for n=1, . . . ,N_(c) associated with the cores inthe multi-core fiber. More specifically, the scrambling configurationdevice 17 may be configured to determine the scrambling function πcorresponding to a two-by-two permutation of said the cores according tothe permutation of at least a first core core_(n) with a second corecore_(m) with n≠m, the first core core_(n) and the second core core_(m)being associated with different core types T_(n)≠T_(m).

In some embodiments in which the multi-core fiber is a heterogeneousmulti-core fiber, the scrambling configuration device 17 may beconfigured to determine the scrambling function π depending on the coretypes T_(n) for n=1, . . . ,N_(c) and the core loss values λ_(n) forn=1, . . . ,N_(c) associated with the N_(c) cores, the scramblingfunction corresponding in such embodiments to a two-by-two permutationof the N_(c) cores according to the permutation of at least a first corecore_(n) with a second core core_(m) with n≠m, the first core core_(n)and the second core core_(m) being associated with different core typesT_(n)≠T_(m) and different core loss values.

The scrambling configuration device 17 may be configured to communicatethe determined scrambling function π to at least one scrambling device133 arranged in the optical transmission channel 13 for scrambling thecores in the multi-core fiber by applying the scrambling function Tr.

In some embodiments in which the optical fiber is a concatenation of Kfiber slices, the optical transmission channel 13 may comprise at leastone scrambling device 133 arranged periodically in the opticaltransmission channel 13 according to a scrambling period denoted byK_(SCT). Accordingly, a scrambling device 133 may be arranged in thek^(th) fiber slice if k is a multiple of the scrambling period.

The scrambling function π may be represented in a two-dimensional formaccording to

${\pi = \begin{pmatrix}{core_{1}} & {core_{2}} & \ldots & {core_{N_{c}}} \\{\pi\left( {core_{1}} \right)} & {\pi\left( {core_{2}} \right)} & \ldots & {\pi\left( {core_{N_{c}}} \right)}\end{pmatrix}},$

where a core core_(i) is permuted with the core core_(j)=π(core_(i)) ofa different type.

The scrambling function π may be represented in a matrix form by apermutation matrix denoted by P, the entries of the permutation matrixare given by:

$\begin{matrix}{P_{ij} = \left\{ \begin{matrix}{{1\mspace{14mu}{if}\mspace{14mu}{\pi\left( {core_{i}} \right)}} = \ {core}_{j}} \\{0\mspace{14mu}{otherwise}}\end{matrix} \right.} & (15)\end{matrix}$

According to some embodiments in which the multi-core fiber isheterogeneous, the scrambling configuration device 17 may be configuredto determine the scrambling function π depending on the core types T_(n)for n=1, . . . ,N_(c) associated with the cores in the multi-core fiberby applying, for example and without limitation, a scrambling techniquechosen in a group comprising a snail scrambling technique, a rotationscrambling technique, and a snake scrambling technique.

In order to apply one of the snail, rotation, and snake scramblingtechniques, the scrambling configuration device 17 may be firstconfigured to classify the cores core-i for i taking value between 1 andN_(c) in a numbered set denoted by

=({core₁,{T₁,λ₁}},{core₃,{T₂,λ₂}},{core₃,{T₃,λ₃}}, . . . ,{core_(N) _(c),{T_(N) _(c) ,λ_(N) _(c) }}) such that each core core_(i) in thenumbered list

is associated with different core types, for i=1, . . . , N_(c).

Using the numbering of the cores in the set

and according to any of the snail, rotation, or snake scramblingtechniques, the scrambling configuration device 17 may determine thescrambling function π such that for each core core_(i) in the set

with i=1, . . . ,N_(c)−1, the core core_(i) is permuted with the coreπ(core_(i))=core_(i+1) and that the core core_(N) _(c) is permuted withthe core π(core_(N) _(c) )=core₁. The scrambling function π isaccordingly expressed in a two-dimensional form as

$\pi = {\begin{pmatrix}{core_{1}} & {core_{2}} & \ldots & {core_{N_{c}}} \\{core_{2}} & {core_{3}} & \ldots & {core_{1}}\end{pmatrix}.}$

Based on this scrambling function, the symbols propagating through thedifferent cores are permuted such that the i^(th) symbol propagatingthrough the core core_(i), propagates after the application of thescrambling function through the core π(core_(i)).

In a first example, the snail scrambling technique corresponds to theapplication of the scrambling rule π(core_(i))=core_(i+1) for i=1, . . .,N_(c)−1 and π(core_(N) _(c) )=core₁ in a heterogeneous multi-core fibercomprising an odd number of cores among which a core is a central coreand the remaining cores are arranged in the edges of the hexagon. Inparticular, depending on the ordering of the cores in the set

, the core core₁ may correspond to the central core.

FIG. 11 is a cross section view of a 7-cores heterogeneous multi-corefiber in which the seven cores are scrambled using a snail scramblingtechnique according to the clockwise direction such that the centralcore is permuted with his neighbor core located on the right side andthat each of the remaining cores is permuted with its left-hand neighborcore of a different type, the core located on the left side of thecentral core being permuted with the central core. The scramblingfunction may be written in this example in the two-dimensional form as

$\pi = \begin{pmatrix}{core_{1}} & {core_{2}} & \ldots & {core_{7}} \\{core_{2}} & {core_{3}} & \ldots & {core_{1}}\end{pmatrix}$

such that core₁ corresponds to the central core and in the matrixrepresentation according to:

$P = \begin{pmatrix}0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$

The symbols s₁,s₂, . . . ,s₇ are accordingly permuted such that afterthe application of the scrambling function, the symbol s₁ propagatesthrough the core core₂, each symbol s_(i) for i=2, . . . ,6 propagatesthrough the core core_(i+1), and the symbol s₇ propagates through thecentral core.

FIG. 12 illustrates a cross section view of a 12-cores heterogeneousmulti-core fiber in which the twelve cores are permuted using a rotationscrambling technique according to the clockwise direction. The cores arearranged in a ring form. Using the rotation scrambling technique, eachcore is permuted with its right-hand neighbor core of a different typesuch that π(core_(i))=core_(i+1) for i=1, . . . ,11 and the core core₁₂is permuted with the core core₁.

FIG. 13 illustrates a cross section view of a 32-cores heterogeneousmulti-core fiber in which the cores are permuted using a snakescrambling technique according to the clockwise direction. The cores arearranged in a two-dimensional grid comprising six layers. The firstupper layer comprises four cores numbered as core₁,core₂,core₃,core₄.The second layer located underside the first layer comprises six coresnumbered as core₅-core₁₀. The third layer located underside the secondlayer comprises six cores numbered core₁₁ core₁₆. The fourth layerlocated below the third layer comprises six cores numbered core₁₇core₂₂. The fifth layer located below the fourth layer comprises sixcores numbered core₂₃ core₂₈. And finally a lower layer comprises fourcores numbered core₂₉ core₃₂. According to the snake scramblingtechnique, each core in each layer is permuted with its right-handneighbor core of a different type, the last core of each layer ispermuted with the first core of the layer located below said each layer,and the core core₃₂ (i.e. the last core of the lower layer) is permutedwith the core core₁ (i.e. with the first core of the upper layer).

FIGS. 11, 12, and 13 illustrate examples of the application of thesnail, rotation, and snake scrambling techniques according to apermutation of the cores in the clockwise direction. However, it shouldbe noted that the snail, rotation, and snake scrambling techniques maybe also applied according to a permutation of the cores in thecounterclockwise direction.

Using the matrix notation of the scrambling function, the optical fibertransmission channel including the scrambling devices 133 can beexpressed according to:

Y=√{square root over (L)}Π_(k=1) ^(K)((H _(XT,k))M _(k) P^((k)))X+N  (16)

In equation (16), the matrix P^((k)) is a N_(c)×N_(c) matrixrepresenting the application of the scrambling function π in the k^(th)fiber span by the k^(th) scrambling device, k being a multiple of thescrambling period.

According to some embodiments, at least one scrambling device 133 may beconfigured to apply the scrambling function π in the electrical field.

In other embodiments, at least one scrambling device 133 may be anoptical device, configured to apply the scrambling function π in theoptical field. Exemplary optical scrambling devices comprise converters,optical multiplexers, optical multiplexing devices, and photoniclanterns.

According to some embodiments, the scrambling configuration device 17may be configured to determine the scrambling function during the phaseof the design of the optical fiber transmission channel prior to theinstallation of the scrambling device(s) 133.

In other embodiments, the scrambling configuration device 17 may beconfigured to determine the scrambling function for the configuration ofone or more scrambling devices 133 in an operating optical transmissionchannel 13.

There is also provided a method for transmitting data in an opticaltransmission system 100 over an optical fiber transmission channel 13made of a multi-core fiber, optical signals carrying data propagatealong the multi-core fiber according to N_(c)≥2 cores, each core beingassociated with one or more core parameters.

FIG. 10 is a flowchart depicting a method of transmitting data over anoptical fiber transmission channel 13, according to some embodimentsusing a single polarization, a single wavelength, a singlecarrier-modulation, a single error correcting code without Space-TimeCoding, and a single-mode multi-core fiber.

At step 1001, parameters of the multi-core fiber may be received. Theseparameters may comprise the number of cores N_(c)≥2, the length L of thefiber, the bending radius R_(b), the number K of fiber slices, thecoupling coefficients k_(n,m) between the cores of the multi-core fiber,the cladding diameter, the radius of each core of the multi-core fiber,the type T_(n) of each core core-n of the multi-core fiber, with n=1, .. . ,N_(c).

At step 1003, a scrambling function π may be determined depending on oneor more of the core parameters associated with the two or more cores ofthe multi-core fiber.

In some embodiments, a core parameter associated with each core core-nmay be chosen in a group comprising a core type T_(n) and a core lossvalue λ_(n).

In some embodiments, the scrambling function π may be determineddepending on the core loss values associated with the cores of themulti-core fiber.

In such embodiments, at step 1003, the core loss value λ_(n) associatedwith each core core-n for n=1, . . . ,N_(c) may be determined. Inparticular, the core loss values associated with the cores of themulti-core fiber may be determined depending on the crosstalkcoefficients and the misalignment losses coefficients according toequation (14).

Given the core loss values associated with each of the cores of themulti-mode fiber, the scrambling function π may be determined forpermuting a core associated with a high core loss value with a coreassociated with a small core loss value.

In some embodiments, the cores core-i for i∈{1, . . . ,N_(c)} may beordered in a numbered list

=({core₁,{T₁,λ₁}},{core₃,{T₂,λ₂}},{core₃,{T₃,λ₃}}, . . . ,{core_(N) _(c),{T_(N) _(c) ,λ_(N) _(c) }}) such that each core core_(i) in thenumbered list

is associated with a core loss value λ_(i) higher than or smaller thanthe core loss value λ_(i+1) associated with the core core_(i+1)depending on the given order considered to order the cores. Given thedetermined order of the core loss values, the scrambling function π maybe determined depending on the order of the core loss values associatedwith the two or more cores.

In an embodiment considering the numbered list of the ordered cores, thescrambling function π may be determined for permuting core core_(i)associated with the i^(th) highest core loss value with the corecore_(N) _(c) _(−i+1) associated with the i^(th) lowest core loss value,with

${i = 1},\ldots\mspace{14mu},\frac{N_{c}}{2}$

for an even number of cores N_(c) and

${i = 1},\ldots\mspace{14mu},\left\lfloor \frac{N_{c}}{2} \right\rfloor$

for an odd number of cores N_(c).

The determination of the scrambling function depending on the core lossvalues associated with the cores of the multi-core fiber may beperformed in embodiments considering a homogeneous or a heterogeneousmulti-core fiber.

In some embodiments in which the multi-core fiber is heterogeneous, thescrambling function may be determined depending on the core types T_(n)for n=1, . . . ,N_(c) associated with the cores in the multi-core fiber.In such embodiments, the scrambling function may be determined for atwo-by-two permutation of the cores according to the permutation of atleast a first core core_(n), with a second core core_(m) with n≠m, thefirst core core_(n) and the second core core_(m) being associated withdifferent core types T_(n)≠T_(m).

In some embodiments, the scrambling function may be determined dependingon the core types using one of the snail, rotation, or the snakescrambling techniques.

In some embodiments, the scrambling function may be determined dependingthe core types T_(n) for n=1, . . . ,N_(c) and the core loss valuesλ_(n) for n=1, . . . ,N_(c) associated with the N_(c) cores, thescrambling function corresponding in such embodiments to a two-by-twopermutation of the N_(c) cores according to the permutation of at leasta first core core_(n) with a second core core_(m) with n≠m, the firstcore core_(n) and the second core core_(m) being associated withdifferent core types T_(n)≠T_(m) and different core loss values.

At step 1005, a permutation of the core of the multi-core fiber may beperformed by applying the scrambling function π. In particular, theapplication of the scrambling function may be performed using the matrixrepresentation of the scrambling function given in equation (15).

At step 1007, the optical signals propagating along the cores of themulti-core fiber may be redistributed (at least once) according to thepermutation of the cores.

The performance of the proposed deterministic scrambling techniques hasbeen evaluated in terms of core dependent loss and the bit error ratesand compared to the performance of existing random scramblingtechniques.

FIGS. 14, 15, and 16 depict diagrams representing the evaluation of thecore dependent loss as a function of the number of required scramblersobtained respectively by applying the snail, the rotation, and the snakescrambling techniques respectively to a 7-core heterogeneous multi-corefiber (illustrated in FIG. 11), a 12-core heterogeneous multi-core fiber(illustrated in FIG. 12), and a 32-cores heterogeneous multi-core fiber(illustrated in FIG. 13). Depicted simulation results show that usingthe proposed deterministic scrambling techniques according to theinvention enables decreasing the number of scramblers/scrambling devicesin the optical fiber transmission system while decreasing the coredependent loss. In particular, a CDL reduction of 2.4 dB can be obtainedby installing only five snail scramblers in the 7-cores heterogeneousmulti-core fiber instead of installing 25 random scramblers. The CDL canbe decreased in the 12-cores multi-core fiber to the minimum value equalto 1.3 dB by installing only 5 deterministic rotation scramblersimplementing the rotation scrambling technique while applying the randomscramblers allows reaching a CDL lower value of 1.5 dB by installing 35random scramblers. And in the 32-cores heterogeneous multi-core fiber,the number of scrambling can be decreased from 35 random scramblers to 5deterministic snake scramblers, both achieving a CDL value of 1.8 dB.

FIGS. 17, 18, and 19 depict diagrams representing the evaluation of thebit error rate performance as a function of the signal-to-noise ratio(SNR) obtained respectively by applying a snail scrambling technique toa 7-core heterogeneous multi-core fiber (illustrated in FIG. 11), arotation scrambling technique to a 12-cores heterogeneous multi-corefiber (illustrated in FIG. 12), and a snake scrambling technique to a32-cores heterogeneous multi-core fiber (illustrated in FIG. 13). A16-QAM modulation is used as the modulation scheme at the opticaltransmitter and Maximum-Likelihood decoding is used at the opticalreceiver. Such simulation results show that the proposed deterministicscrambling techniques according to the various embodiments of theinvention achieve better BER performance than the existing randomscrambling techniques and the no-scrambling configurations, and approachthe performance of the CDL free transmission channel (referred to as the‘Gaussian Channel’). More specifically, installing 5 snail scramblersimplementing the deterministic snail scrambling technique in the 7-coresfiber enables decreasing the SNR penalty compared to the CDL-freechannel to 0.5 dB instead of 1 dB at BER=10⁻³ by applying the randomscramblers. In the example of the 12-cores fiber, installing 5deterministic rotation scramblers implementing the rotation scramblingtechnique enables completely mitigating the core dependent loss, whilerandom scramblers have a 1.5 dB of SNR penalty compared to the CDL-freechannel. Performance gains are also obtained for the 32-cores multi-corefiber using the snake scrambling technique as illustrated in FIG. 19.The transmission system without scrambling has a SNR penalty equal to2.5 dB at BER=10⁻⁴. Installing the random scramblers decreases thispenalty to 0.4 dB, while applying the snake scrambling technique byinstalling 5 deterministic snake scramblers enables reducing the SNRpenalty to 0.1 dB.

Although the various embodiments have been described in connection tosingle-core multi-mode fibers in which a single polarization, a singlewavelength and single-carrier modulation are used, it should be notedthat the invention can also be applied in multi-core multi-mode fibersin combination with polarization multiplexing using two polarizationsand/or in combination with the use of wavelength multiplexing usingseveral wavelengths, and/or using multi-carrier modulation formats.

Further, the invention is not limited to communication applications andmay be integrated in other applications such as data storage and medicalimaging. The invention may be used in several optical transmissionsystems, for example automotive industry applications, in oil or gasmarkets, in aerospace and avionics sectors, sensing applications, etc.

While embodiments of the invention have been illustrated by adescription of various examples, and while these embodiments have beendescribed in considerable details, it is not the intent of the applicantto restrict or in any way limit the scope of the appended claims to suchdetails. Additional advantages and modifications will readily appear tothose skilled in the art. The invention in its broader aspects istherefore not limited to the specific details, representative methods,and illustrative examples shown and described.

1. An optical transmission system comprising an optical transmitterconfigured to transmit data over an optical fiber transmission channelmade of a multi-core fiber, optical signals carrying said data propagatealong the multi-core fiber according to two or more cores, each corebeing associated with one or more core parameters, wherein the opticaltransmission system comprises: a scrambling configuration deviceconfigured to determine a scrambling function depending on one or moreof the core parameters associated with said two or more cores, and atleast one scrambling device arranged in said optical fiber transmissionchannel for scrambling said two or more cores, each of said at least onescrambling device being configured to determine permuted cores byapplying said scrambling function to said two or more cores and toredistribute said optical signals according to said permuted cores. 2.The optical transmission system of claim 1, wherein a core parameterassociated with each core is chosen in a group comprising a core typeand a core loss value.
 3. The optical transmission system of claim 2,wherein the scrambling configuration device is configured to determinethe core loss value associated with each core depending on at least onecrosstalk coefficient and at least one misalignment loss value, acrosstalk coefficient representing the crosstalk between said each coreand a neighbor core to said each core, a misalignment loss valuerepresenting a misalignment of the multi-core fiber.
 4. The opticaltransmission system of claim 2, wherein the scrambling configurationdevice is configured to order said two or more cores according to agiven order of the core loss values associated with said two or morecores, the scrambling configuration device being configured to determinesaid scrambling function depending on the order of the core loss valuesassociated with said two or more cores.
 5. The optical transmissionsystem of claim 4, wherein the number of said two or more cores in themulti-core fiber is an even number, said scrambling configuration devicebeing configured to determine said scrambling function for permuting thetwo or more cores two-by-two according to the permutation of the coreassociated with the i^(th) highest core loss value with the coreassociated with the i^(th) lowest core loss value, with i beingcomprised between 1 and the half of the number of cores in saidmulti-core fiber.
 6. The optical transmission system of claim 4, whereinthe number of said two or more cores in the multi-core fiber is an oddnumber, said scrambling configuration device being configured todetermine said scrambling function for permuting the two or more corestwo-by-two according to the permutation of the core associated with thei^(th) highest core loss value with the core associated with the i^(th)lowest core loss value, with i being comprised between 1 and the floorpart of half the number of cores in said multi-core fiber.
 7. Theoptical transmission system of claim 4, wherein the multi-core fiber isan homogeneous multi-core fiber, the two or more cores being associatedwith an identical core type.
 8. The optical transmission system of claim4, wherein the multi-core fiber is an heterogeneous multi-core fiber, atleast two of said two or more cores being associated with different coretypes.
 9. The optical transmission system of claim 2, wherein themulti-core fiber is an heterogeneous multi-core fiber, the scramblingconfiguration device being configured to determine said scramblingfunction depending on the core types associated with said two or morecores, said scrambling function corresponding to a two-by-twopermutation of said two or more cores according to the permutation of atleast a first core with a second core, the first core and the secondcore being associated with different core types.
 10. The opticaltransmission system of claim 2, wherein the multi-core fiber is anheterogeneous multi-core fiber, the scrambling configuration devicebeing configured to determine said scrambling function depending on thecore types and the core loss values associated with the two or morecores, said scrambling function corresponding to a two-by-twopermutation of said two or more cores according to the permutation of atleast a first core with a second core, the first core and the secondcore being associated with different core types and different core lossvalues.
 11. The optical transmission system of claim 1, wherein said atleast one scrambling device is configured to apply said scramblingfunction in the electrical field or in the optical field, a scramblingdevice configured to apply said scrambling function in the optical fieldbeing chosen in a group comprising optical converters, opticalmultiplexers, optical multiplexing devices, and photonic lanterns. 12.The optical transmission system of claim 1, wherein at least one of saidtwo or more cores is a multi-mode core comprising two or more spatialpropagation modes.
 13. The optical transmission system of claim 1,wherein the optical transmitter comprises: an error correcting codeencoder configured to encode said data into a codeword vector byapplying at least one error correcting code; a modulator configured todetermine a set of modulated symbols by applying a modulation scheme tosaid codeword vectors, and a Space-Time encoder configured to determinea codeword matrix by applying a Space-Time code to said set of modulatedsymbols.
 14. A method for transmitting data in an optical transmissionsystem over an optical fiber transmission channel made of a multi-corefiber, optical signals carrying said data propagate along the multi-corefiber according to two or more cores, each core being associated withone or more core parameters, wherein the method comprises scramblingsaid two or more cores, said step of scrambling comprising: determininga scrambling function depending on one or more of the core parametersassociated with said two or more cores; determining a permutation ofsaid two or more cores by applying said scrambling function, andredistributing said optical signals according to said permutation of thetwo or more cores.